18.440 Probability and Random Variables: Fall, 2012
Lectures: MWF 1011, 34101
Office hours: Wednesday 24, 2180
TA: Ruthi Hortsch
TA office hours: Thursday 35, 2251
Text: A First Course in Probability, 8th edition, by Sheldon Ross.
(Here's another free
and funtoread book you might enjoy.)
Assignments: Homeworks (20%), midterm exams (40%), final exam (40%)
Final
exam schedule hosted at registrar
Stellar course web site
TENTATIVE SCHEDULE

Lecture 1 (September 5): 1.11.3 Permutations and
combinations
(also Pascal's
triangle  as
studied (not invented) by Pascal, see also
correspondence with Fermat).
 Lecture
2 (September 7): 1.41.5 Multinomial coefficients
and more
counting (see
Pascal's pyramid)
Problem Set One, due September
14

Lecture 3 (September 10): 2.12.2 Sample spaces and set
theory

Lecture 4 (September 12): 2.32.4 Axioms of probability (see
Paulos' NYT article and a famous hat
problem)

Lecture 5 (September 14): 2.52.7 Probability and equal likelihood
(and a bit more
history )
Problem Set Two, due September
19

Lecture 6 (September 17): 3.13.2
Conditional probabilities

Lecture 7 (September 19): 3.33.5 Bayes' formula and independent
events
Problem Set Three, due
September
28

Lecture 8 (September 24): 4.14.2 Discrete random variables

Lecture 9 (September 26): 4.34.4 Expectations of discrete random
variables (and, for nondiscrete setting, examples of nonmeasurable sets,
as in the Vitali construction)

Lecture 10 (September 28): 4.5 Variance
Problem Set Four, due
October 5

Lecture 11 (October 1): 4.6 Binomial random variables, repeated
trials and the socalled Modern Portfolio Theory.

Lecture 12 (October 3): 4.7 Poisson random variables

Lecture 13 (October 5): 9.1 Poisson processes
Practice Midterm Exam
with partial solutions (here is an old
midterm
and 2009 Midterm One With
Solutions
)

Lecture 14 (October 10): 4.84.9 More discrete random variables

Lecture 15 (October 12): REVIEW
Spring
2011 midterm exam
on Chapters 14 (plus 9.1) with
solutions .
Fall
2011 midterm exam
on Chapters 14 (plus 5.15.4
and 9.1) with
solutions .

Lecture 16 (October 15): FIRST
MIDTERM with
solutions.

Lecture 17 (October 17): 5.15.2 Continuous random variables

Lecture 18 (October 19): 5.3 Uniform random variables
Problem Set Five, due October
26

Lecture 19 (October 22): 5.4 Normal random variables

Lecture 20 (October 24): 5.5 Exponential
random variables

Lecture 21 (October 26): 5.65.7 More continuous random variables
Problem Set Six, due November
2

Lecture 22 (October 29): 6.16.2 Joint distribution functions

Lecture 23 (October 31): 6.36.5 Sums of independent random
variables

Lecture 24 (November 2): 7.17.2 Expectation of sums
Problem Set Seven, due
November 9

Lecture 25 (November 5): 7.37.4 Covariance and correlation.
REMARK: To see how society understands
correlation and causation, try typing "study"
and "linked to" into google and page through until you find 100 distinct
headlines roughly of the form "Study links A to B". Guess how many
are real correlations (as opposed to statistical flukes or chance
anomalies or measurement/methodology errors
that might not appear
in a larger,
more careful study).
In how many cases did the journalist provide the information you'd need
to assess (1) the strength of the evidence for
correlation existence (2) the magnitude of the reported correlation (3)
what is known about the plausibility of the most obvious causal and
noncausal explanations?

Lecture 26 (November 7): 7.57.6 Conditional expectation

Lecture 27 (November 9): 7.77.8 Moment generating distributions
Practice Midterm Exam Two
with
partial solutions and 2009 Midterm Two
with solutions
.
Spring 2011 Second midterm exam on 17 (plus 9.1) with
solutions.
Fall 2011 second midterm with solutions

Lecture 28 (November 14): REVIEW

Lecture 29 (November 16):
SECOND
MIDTERM with
solutions
Problem Set Eight, due
November 21

Lecture 30 (November 19): 8.18.2 Weak law of large numbers

Lecture 31 (November 21): 8.3 Central limit theorem
Problem Set Nine, due November 30

Lecture 32 (November 26): 8.48.5 Strong law of large numbers (see
also
the truncationbased proof on Terry Tao's blog and the characteristic
function proof of the weak law) and Jensen's inequality.

Lecture 33 (November 28): 9.2 Markov chains

Lecture 34 (November 30): 9.39.4 Entropy
Problem Set Ten, due December
7
(plus
martingale note)

Lecture 35 (December 3): Martingales and the
Optional Stopping Time
Theorem
(see also prediction market plots)

Lecture 36 (December 5): Risk Neutral Probability and BlackScholes
(look up options quotes at the Chicago Board Options Exchange)

Lecture 37 (December 7): REVIEW

Lecture 38 (December 10:) REVIEW

Lecture 39 (December 12): REVIEW
Practice Final Problems
(covering
only later portion of the course) with
partial solutions and Spring 2011
Final
with
solutions .
 December 1721 (date TBA):
Final exam